# W Bosons Elementary, but decay?

1. ### Goodies

10
I'm a little confused.

During Beta(-) radiation, a neutron becomes a proton due to a down quark becoming an up quark. When this happens, a W(-) boson is emitted which almost immediately decays into an electron and an electron antineutrino. A W(+) boson, similarly, is emitted when a down quark turns into an up quark and decays into a positron and an electron neutrino. If a W boson is an elementary particle, how does it decay into these?

Thanks, guys! It's a huge help!

### Staff: Mentor

There are many unstable fundamental particles. As long as a particle has enough mass, it can decay into other particles, provided it does so in a way that conserves energy (including mass energy), momentum, spin, and charge.

Perhaps you think that if a W decays into an electron and an electron antineutrino that somehow the electron and antineutrino must have been "inside" the W to begin with. That is not the case. All that is necessary is for the conservation laws to be satisfied.

### Staff: Mentor

You might as well have asked the same thing about the up-quark inside the proton which "decays" into a down-quark (thereby converting the proton into a neutron) and a W boson. Or about a mu- which decays into an electron, a muon-neutrino, and an electron-antineutrino.

4. ### ohwilleke

685
A key point to understand is that while emission of a W- boson by a down quark that transforms the down quark into an up quark, which W- decays into an electron and an electron antineutrino with or without a photon, is the "usual" form that beta decay takes when no other decay paths are possible due to a lack of energy-momentum in the system, if the emitting down quark is sufficiently energetic, other possibilities can and do occur.

For example, the W- could decay instead into a muon and muon antineutrino, or a tau lepton and tau antineutrino, rather than an electron and and electron anti-neutrino.

In general, any possible decay of a W- boson that preserves a number of conserved quantities (e.g. baryon number, lepton number, lepton flavor number, electric charge, angular momentum, and net color charge) is possible and has a predictable probability which is at the first order equal for all possibilities, when the aggregate rest mass of the post-W- boson decay system is less than or equal to the pre-emission mass-energy of the system, and the equations of the weak force spell out precisely how likely each possibility is and how rapidly the decay will take place, etc. This is possible even if an intermediate state in the decay chain is seemingly prohibited by mass-energy conservation in which case the particles in the intermediate states are called "virtual particles."

The weak hypercharge of a particle, in turn, determines its probability of emitting or absorbing a W boson.

The same general principles also apply to the emission and absorption of Z bosons.

In general, a particle is fundamental in the Standard Model when its properties cannot be determined from first principles from the Standard Model equations and other particle properties (although in some cases the number of available degrees of freedom can be localized in different ways - for example, you can determine any one of the parameters (1) Weinberg angle, (2) the W boson mass and (3) the Z boson mass from the other two parameters).

No equation in the Standard Model can tell you, a priori without experimentally measurements of these parameters, the charm quark mass, or the probability that a charm quark that emits a W boson will become a down quark (which it does about 5% of the time) rather than a strange quark (which it does almost 95% of the time). In contrast, it is possible in principle to determine the exact mass of a proton from the equations of the Standard Model and the properties of up and down quarks and gluons and electrons, and this has in fact been done to a precision of about 1% (it turns out that precision measurements of small quantities on a percentage accuracy basis is harder than precision measurements of large quantities like the top quark or tau lepton mass).

Put another way, in the Standard Model, the only deeper kind of stuff is mass-energy and other conserved quantum numbers that are not summed up in a particular kind of particle.

5. ### Goodies

10
Huge, huge thanks to ohwilleke for the complete, specific answer. Greatly appreciated.
@jtbell
I thought of bosons as almost virtual in comparison to quarks and other fundamental particles. This is probably due to my misunderstanding of how they can "carry forces", but like I said, I'm a novice at all of this so I'm still learning!

6. ### ohwilleke

685
The mean lifetime of a W or Z boson is on the order of 10^-25 seconds. While gluons, having zero rest mass, can in principle exist indefinitely, in practice, they last only so long as it takes to cross from one side of a proton or neutron or other multi-quark particle to the other at approximately the speed of light, which works out to be on the order of 10^-22 seconds or so. Higgs bosons live longer than W or Z bosons but only a couple of orders of magnitude longer. The only boson in the Standard Model which typically has a long lifetime is the photon which travels at the speed of light until it hits something. Hypothetical gravitons would be similarly long lived.

Standard Model bosons are often not "virtual" but except for photons, are almost always ephemeral (i.e. very short lived).